I do not, as a rule, attempt to enlarge with exact accuracy from a small sketch. I prefer to have some license to modify the design. However, at times scales for enlarging and reducing can be very useful, particularly if the beginner wishes to copy some given design. Students often use reducing scales when working from the live model. You should try to train your eye and not to resort to scales and measurements unless really necessary. If your drawing is weak, it is possible to work with a few guiding measurements and then to try and use your eyes and judgment. Temperaments vary in these matters and some will enjoy making very accurate and meticulous copies. This, however, can be paralyzing to creative thought and design.
I describe in this chapter a few simple methods of enlarging and reducing by linear measurement, using the squaring-up method and angle scales. A number of other methods, such as the pointing machine, the pantograph, the three-caliper-and-post method, proportional dividers, and the wooden-frame method, will be found in publications on the methods of sculptors.
Enlarging a design for relief by squaring-up
This is a very old method which can be used for enlarging or reducing. Examine the diagram of the cat design (Fig. 2). Draw a rectangle to the required size. This should be in the same proportion in length and breadth as the small design. First draw the diagonals from A to D, and then from B to C. This will give you the center O. Draw lines EF and GH. Again draw the diagonals EH, FH, GE, and GF. This will give you the position of the vertical lines WX and YZ. Continue this process until the units are small enough to give accuracy in drawing. Now number the vertical and horizontal lines. By noting carefully where the drawing crosses the line pattern you will be able to enlarge the design with ease.
Enlarging by using the angle scale
The angle scale for both enlarging and reducing is very simple to use as soon as the principle is understood. Figure 2 shows a diagram showing the enlargement of a fish design to 1 1/2 times. In this scale any two measurements can be used for making the angle, providing that the ratio is the same: for instance, 4 in. and 6 in., 6 in. and 9 in., or 9 in. and 13 1/2 in. If you take the first two measurements suggested, proceed as follows:
Enlarging 1 1/2 times. Draw a line AB, 4 in. in length. Set the calipers or pencil compasses at 4 in. and from point B describe arc O. Set the calipers at 6 in. and from point A describes an arc intersecting arc O at point C. Draw line AC. Any given measurement on the small design, as for instance AX on the fish’s head, should be taken along the line AB once only, then up from X to intersect line AC at point X. From this point of intersection down to A is the 1 1/2 enlargement.
Enlarging to 2 1/2 times. Make the angle as shown in the illustration for this scale. The only difference from the 1 1/2scale is that in this case you must measure twice along AB before intersecting AC in making the angle, and in every subsequent measurement to be enlarged.
If the enlargement is to be over 3 times you must then measure 3 times on line AB.
Enlarging scales for odd sized blocks.
If you have an odd sized block of wood, say, 13 in. high, and you wish to work from a model 8 in. high, you can make an open scale. Proceed to take measurements as in the scale for 1 1/2times enlargement. Again I would mention that if the block is over twice the height of your model, it will be necessary to measure twice along the line AB before intersecting AC.
Half scale reduction. The angle reducing scale is very simple to make and easy to use. In the case of the elephant (Fig. 3) all measurements are to be reduced by half for carving the animal half size. To make this scale, draw the line AB 12 in. in length. With the calipers at 12 in. on point A describe an arc from B. Set the calipers at 6 in. and from B describe another arc to cross the first at C. Make the angle by drawing a line from A to C. Any measurement, as for instance A to H on the large elephant is taken by the calipers and an arc described from A across the angle: in this measurement it is the arc XH, and gives the height of the elephant and base in the small block.
This scale can be used in any size of reduction. Other examples given here are for 1/4 and 3/4 reductions. Providing AB and BC are at the ratios you require, the measurements are arbitrary. For example, you can use the height of the model to be reduced as the long measurement, and the height of the small block of wood as the short measurement. By using the angle scale so produced, it is simple to test the block for other dimensions. In this way you can find out whether the block is a suitable shape for the figure you wish to reduce. If the figure and block are both too large for measurement by the calipers, divide both lengths by a half or quarter. For example, in the case of a figure of 4 ft. 4 in. in height and a block of 3 ft. you can make the angle by using the length 1 ft. 1 in. and 9 in., a quarter division of both measurements.
The plumb-bob, square and set-square can be used as aids for measurements in depth. The caliper points can also be crossed for taking interior measurements (Fig. 4).